In [1]}, we performed several computer simulations with dense lattices (e.g. \(E_8\) ) and MIMO lattices
(such as the ones considered in [2]}), which are typically not dense in low to moderate dimensions.
We aimed at minimizing the number of parameters in a standard fully-connected feed-forward sigmoid neural network [3]} while maintaining quasi-MLD performance. The training was performed with usual gradient-descent-like techniques [3]}. The network considered is shallow, similar to the HLD, as it contains only three hidden layers.
Let \(W\)  be the number of parameters in the neural networks (i.e. the number of edges).
To be competitive, \(W\)  should be smaller than \(2^n\) . For \(E_8\)  we obtained a complexity ratio \(\frac{\log _2 W}{n}=2.0\)  whereas for the MIMO lattice the ratio is \(\frac{\log _2 W}{n}=0.78\) .
